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Honam Mathematical Journal
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Volume 36, Issue 4 - Dec 2014
Volume 36, Issue 3 - Sep 2014
Volume 36, Issue 2 - Jun 2014
Volume 36, Issue 1 - Mar 2014
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CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE
Ucum, Ali ; Ilarslan, Kazim ; Karakus, Siddika Ozkaldi ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 475~492
DOI : 10.5831/HMJ.2014.36.3.475
In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space
also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.
DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA
Choi, Seul Hee ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 493~503
DOI : 10.5831/HMJ.2014.36.3.493
We consider the simple antisymmetrized algebra
. The simple non-associative algebra and its simple subalgebras are defined in the papers , , , , , , . Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers , , , , , , , , . We find all the derivations of the Lie subalgebra
in this paper.
JORDAN HIGHER CENTRALIZERS ON SEMIPRIME RINGS AND RELATED MAPPINGS
Jung, Yong-Soo ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 505~517
DOI : 10.5831/HMJ.2014.36.3.505
We prove that every Jordan higher left (right) centralizer on a 2-torsion free semiprime ring is a higher left (right) centralizer which is to generalize the result of Zalar .
REMARKS ON SIMPLY k-CONNECTIVITY AND k-DEFORMATION RETRACT IN DIGITAL TOPOLOGY
Han, Sang-Eon ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 519~530
DOI : 10.5831/HMJ.2014.36.3.519
To study a deformation of a digital space from the viewpoint of digital homotopy theory, we have often used the notions of a weak k-deformation retract  and a strong k-deformation retract [10, 12, 13]. Thus the papers [10, 12, 13, 16] firstly developed the notion of a strong k-deformation retract which can play an important role in studying a homotopic thinning of a digital space. Besides, the paper  deals with a k-deformation retract and its homotopic property related to a digital fundamental group. Thus, as a survey article, comparing among a k-deformation retract in , a strong k-deformation retract in [10, 12, 13], a weak deformation k-retract in  and a digital k-homotopy equivalence [5, 24], we observe some relationships among them from the viewpoint of digital homotopy theory. Furthermore, the present paper deals with some parts of the preprint  which were not published in a journal (see Proposition 3.1). Finally, the present paper corrects Boxer's paper  as follows: even though the paper  referred to the notion of a digital homotopy equivalence (or a same k-homotopy type) which is a special kind of a k-deformation retract, we need to point out that the notion was already developed in  instead of  and further corrects the proof of Theorem 4.5 of Boxer's paper  (see the proof of Theorem 4.1 in the present paper). While the paper  refers some properties of a deck transformation group (or an automorphism group) of digital covering space without any citation, the study was early done by Han in his paper (see the paper ).
THE INCOMPLETE LAURICELLA AND FIRST APPELL FUNCTIONS AND ASSOCIATED PROPERTIES
Choi, Junesang ; Parmar, Rakesh K. ; Chopra, Purnima ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 531~542
DOI : 10.5831/HMJ.2014.36.3.531
Recently, Srivastava et al.  introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function
of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.
HYPER-CONJUGATE HARMONIC FUNCTION ON DUAL OCTONION VARIABLES
Lim, Su Mi ; Shon, Kwang Ho ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 543~553
DOI : 10.5831/HMJ.2014.36.3.543
The aim of this paper is to define hyperholomorphic functions with dual octonion variables on
in another way. Using condition of harmonicity, we research properties of functions of dual octonion variables in Clifford analysis.
FALLING FUZZY BCI-COMMUTATIVE IDEALS
Jun, Young Bae ; Song, Seok-Zun ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 555~568
DOI : 10.5831/HMJ.2014.36.3.555
On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced. Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCI-commutative ideals are provided. Characterizations of a falling fuzzy BCI-commutative ideal are established, and conditions for a falling fuzzy (closed) ideal to be a falling fuzzy BCI-commutative ideal are considered.
A NEW FORM OF FUZZY GENERALIZED BI-IDEALS IN ORDERED SEMIGROUPS
Khan, Hidayat Ullah ; Sarmin, Nor Haniza ; Khan, Asghar ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 569~596
DOI : 10.5831/HMJ.2014.36.3.569
In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (
)-fuzzy subsystems of ordered semigroups namely (
)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (
)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (
)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.
THE EXISTENCE OF WARPING FUNCTIONS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B)
Jung, Yoon-Tae ; Lee, Ga-Young ; Kim, A-Ryong ; Lee, Soo-Young ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 597~603
DOI : 10.5831/HMJ.2014.36.3.597
In this paper, we prove the existence of warping functions on Riemannian warped product manifolds with fiber manifold of class (B) having some prescribed scalar curvatures.
ON A CLASS OF GORENSTEIN IDEALS OF GRADE FOUR
Cho, Yong S. ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 605~622
DOI : 10.5831/HMJ.2014.36.3.605
We provide a minimal free resolution for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection J of grade 3 and a perfect ideal I of grade 3 with type 2 and
> 0 geometrically linked by a regular sequence, where I is generated by odd elements.
CLASSIFICATIONS OF (α, β)-FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS
Jun, Young Bae ; Ahn, Sun Shin ; Lee, Kyoung Ja ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 623~635
DOI : 10.5831/HMJ.2014.36.3.623
Classications of (
)-fuzzy subalgebras of BCK/BCI-algebras are discussed. Relations between (
)-fuzzy subalgebras and (
)-fuzzy subalgebras are established. Given special sets, so called t-q-set and t-
-set, conditions for the t-q-set and t-
-set to be subalgebras are considered. The notions of
-fuzzy subalgebra and
-fuzzy subalgebra are introduced. Conditions for a fuzzy set to be an
-fuzzy subalgebra, a
-fuzzy subalgebra and a
-fuzzy subalgebra are considered.
NOTES ON ALMOST KENMOTSU THREE-MANIFOLDS
Cho, Jong Taek ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 637~645
DOI : 10.5831/HMJ.2014.36.3.637
We study 3-dimensional non-unimodular Lie groups with a left-invariant almost Kenmotsu structure.
COMBINATORIC CONVOLUTION SUMS CONTAINING σ AND
OF THE FORM 2
Kim, Daeyeoul ; Park, Joongsoo ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 647~657
DOI : 10.5831/HMJ.2014.36.3.647
In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when
. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.
THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION
Chung, Young-Bok ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 659~668
DOI : 10.5831/HMJ.2014.36.3.659
In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a
smoothly bounded finitely connected domain in the complex plane.
FUNCTIONS ON κ-NET CONVERGENCE STRUCTURES
Cho, Myung Hyun ; Kim, Junhui ; Moon, Mi Ae ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 669~678
DOI : 10.5831/HMJ.2014.36.3.669
We investigate various properties of
-net convergence structures and define a
-net-based continuous function on
-convergence structures, and study relationships between continuity and
-net-based continuity on
-convergence structures. We also provide some characterizations of
SOME CONVERGENCE THEOREM FOR AND RANDOM VARIABLES IN A HILBERT SPACE WITH APPLICATION
Han, Kwang-Hee ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 679~688
DOI : 10.5831/HMJ.2014.36.3.679
The notion of asymptotically negative dependence for collection of random variables is generalized to a Hilbert space and the almost sure convergence for these H-valued random variables is obtained. The result is also applied to a linear process generated by H-valued asymptotically negatively dependent random variables.
ON THE SUM OF CERTAIN MULTIPLICATIVE FUNCTIONS
Kim, Insuk ; Jun, Sungtae ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 689~694
DOI : 10.5831/HMJ.2014.36.3.689
We find an asymptotic formula of the sum of multi-plicative functions with Dirichlet inversion formula.
UTILITY OF DIGITAL COVERING THEORY
Han, Sang-Eon ; Lee, Sik ;
Honam Mathematical Journal, volume 36, issue 3, 2014, Pages 695~706
DOI : 10.5831/HMJ.2014.36.3.695
Various properties of digital covering spaces have been substantially used in studying digital homotopic properties of digital images. In particular, these are so related to the study of a digital fundamental group, a classification of digital images, an automorphism group of a digital covering space and so forth. The goal of the present paper, as a survey article, to speak out utility of digital covering theory. Besides, the present paper recalls that the papers [1, 4, 30] took their own approaches into the study of a digital fundamental group. For instance, they consider the digital fundamental group of the special digital image (X, 4), where X :=
which is a simple closed 4-curve with eight elements in
, as a group which is isomorphic to an infinite cyclic group such as (Z, +). In spite of this approach, they could not propose any digital topological tools to get the result. Namely, the papers [4, 30] consider a simple closed 4 or 8-curve to be a kind of simple closed curve from the viewpoint of a Hausdorff topological structure, i.e. a continuous analogue induced by an algebraic topological approach. However, in digital topology we need to develop a digital topological tool to calculate a digital fundamental group of a given digital space. Finally, the paper  firstly developed the notion of a digital covering space and further, the advanced and simplified version was proposed in . Thus the present paper refers the history and the process of calculating a digital fundamental group by using various tools and some utilities of digital covering spaces. Furthermore, we deal with some parts of the preprint  which were not published in a journal (see Theorems 4.3 and 4.4). Finally, the paper suggests an efficient process of the calculation of digital fundamental groups of digital images.